Thermodynamic behaviour of some electrolytes in ethane-1,2-diol from - 10 to + 80°C

FULVIO COKRADINI, LUIGI MARCHESELLI, LORENZO TASSI,' AND GIUSEPPE TOSI Depnrttnetzt of Chetni.stt-y. Urziversiiy of Modetza, via G . Catnpi, 183 41100 Morletza, Italy

AND

SALVATOREFANALI Istitrlto di Cronzatogr-afia del Consiglio Ntrziotzale rlelln Ricerche. Area della Ricercn cli Romn,

C.P. 10, 00016 Monterotorldo Scnlo. Rotne. Italy

Received December 22, 1992

FULVIO CORRAI)INI, LUIGI MARCHESELLI, LORENZO TASSI. GIUSEPPE TOSI. and SALVATORE FANALI. Can. J. Che~n. 71, 1265 ( 1993).

Conductivities of the electrolytes NaBr, NaPi, HPi, NaBPh,. and Ph,PBr in ethane-1,2-diol were determined in the - 10 5 t 5 +80°C temperature range. The experimental data were analyzed by the Fuoss-Hsia equation, which pro- vides further informative parameters such as the dissociation constant ( K ) of the ion pairs formed in solution, the lim- iting equivalent conductivity (A,), and the ion-size parameter ( 0 ) . Therrnodynamic behaviour of these electrolytes was derived from analysis of the K values. Single-ion conductivities were evaluated on the basis of the assumption of Ph,PBPh, as reference electrolyte.

Fu~vro CORRADINI, LUIGI MARCHESEI-LI, LORENZO TASSI, GIUSEPPE TOSI et SALVATORE FANALI. Can. J . Chem. 71, 1265 ( 1993).

On a determink la conductivitC des Clectrolytes NaBr, NaPi, HPi, NaBPh, et Ph,PBr dans 1'Cthane-1,2-diol, i des temperatures allant de - 10 B +8O0C. On a analysk les donnCes par l'kquation de Fuoss-Hsia qui fournit d'autres para- mktres plus utiles, comlne la constante de dissociation ( K ) des paires d'ions qui se forn~ent en solution, la conductivitk Cquivalente limite (A,) et le paranlktre de la grosseur de I'ion (2). On a dCrivC le comportement ther~nodynamique de ces Clectrolytes par une analyse des valeurs de K. On a Cvaluk les conductivitCs des ions uniques en se basant sur I'hy- pothkse que le Ph,PBPh, est 1'Clectrolyte de rCfCrence.

[Traduit par la ridaction]

Introduction

Ethane-1,2-diol (ED) has attracted much attention in re- cent years as a nonaqueous solvent for many electrochemi- cal investigations as well as for various practical applications (1) . The great interest that this medium holds for many au- thors can probably be ascribed to its unusual chemical- physical which make it a very singular solvent. ED is amphiprotic in nature, thoroughly miscible with a va- riety of other solvents (polar, such as water, and quasi-apo- l a , such as dioxane); because of its high density and viscosity it may be considered an excellent viscoelastic regulating medium for reaction bath and as thermoregulator fluid. Fur- ther, its high dipole moment (p = 2.28 D) (2) and a mod- erately high dielectric constant (E = 40.97 at 25°C) (3) cause it to be placed between the dissociating solvents in the gen- eral classification of Charlot and TrCmillon (4).

Although a number of precise conductivity measurements of electrolytes in other solvents are reported in the litera- ture, relatively few such studies have been made on ethane- 1,2-diol. Now, following our interest in this field, an attempt has been made to investigate the nature of ion-ion and ion- solvent interactions of such electrolytes as sodium picrate (NaPi), NaBr, NaBPh,, Ph,PBr (all ionophore solutes be- cause of their ionic structure in the crystalline state), and the ionogen picric acid (HPi) dissolved in ED, through the measurement of their conductivities at 19 temperatures ranging from - 10 to +SO°C.

Since few transference-number data for E D solutions of these salts are available in the literature, single-ion conduc-

' ~ u t h o r to whom correspondence may be addressed.

tivities have been evaluated employing the two reference tetraphenyl derivative electrolytes, in an effort to provide reliable values of ionic mobilities.

Experimental section

Mrrret-inls The solvent ethane-1.2-diol (containing less than 0.10% g of

water, as determined by Karl-Fischer titrations) was high purity grade reagent from Carlo Erba (Milan). It was stored over 3A mo- lecular sieves for Inany days before use and the final purity was checked by gas chromatography, confirming the absence of other significant organic components. The solvent has a density of 1.1099 13 g c i n ' , viscosity 17.14 cP, and a specific conductivity of 0.255 FS cin-' at 25OC.

The NaBr was from Aldrich Chemicals, of Suprapure guaran- teed quality, and was utilized without further purification after desiccation at 105°C and preservation in vacuo over PzO, prior to use.

Tetraphenylphosphonium bromide (Fluka) was purified by re- crystallization (X2) from a binary mixture of acetone and 2-pro- panol (v:v 9: I), while NaBPh, (Fluka) was recrystallized (x2) from pure acetone. Both salts were dried at 80°C and preserved in vacuo over P2O5 for some time before use.

Sodium picrate was prepared from picric acid and NaOH, start- ing from their equimolar solutions in water-ethanol (v: v 1 : 1) and working at high temperature. The precipitate was filtered and washed many times with the same solvent mixture and dried in vacuo over P,O,. The final product was checked by elemental analysis before use and the results are reported here: Anal. calcd. for C6H,N3O7Na: C 28.70, N 16.74, H 0.80%; found: C 28.42, N 16.81, H 0.75%.

Appnrnrzls ntld proc.cxlzrres Conductivity measurenlents were made by a Wayne Kerr 6425

Precision Component Analyzer, operating in the 2.5 X 10-'-10 S

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1266 CAN. J . CHEM. VOL. 71, 1993

TABLE 1. Experimental dissociation constant values (K mol-' dm-3) for some electrolytes in ethane- 1,2-diol at different temperatures

NaBPh, Ph,PBr NaBr NaPi HPi tl°C K x lo2 K x 10' K x 10' K x 10' K x lo3

TABLE 2. Coefficients a , and standard deviations u(ln K) of eq. [2] for some elec- trolytes in ethane-1,2-diol

Solute a0 a I fl' a3 10'u(ln K)

NaBPh, - 1844.9 -0.68700 38575 336.57 4.7 Ph,PBr -3343.4 -1.1265 77838 599.43 6.0 NaBr -1705.5 -0.61055 37539 308.79 3.7 NaPi -2358.4 -0.84134 51784 427.03 7.5 HPi -279.43 -0.12219 4310.9 51.839 5.4

range (end scale), with a sensitivity t 0 . 0 1 nS, and employing are given in Tables 1-5 of the Supplementary ater rial' platinized platinum electrodes (cell constant k = 10.538 cm) with available for NaBPh,, Ph,PBr, NaBr, NaPi, and HPi, re- a field frequency of 1 kHz. The measuring cell was embedded in spectively. ~h~ data were analyzed by means of the more a polyurethane protective jacket, and the temperature control was general Fuoss-Hsia equation (6, 7): provided by a Lauda K2R thermostatic bath maintained to within 0 . 0 2 " C over the investigated temperature range. [ I ] A = A, - s(cy)'/' + Ecylgcy

The constancy of temperature was checked by a thermoresis- tance Pt 100 (Tersid, Milan) immersed in the sample in the mea- + J I cy - ~ ~ ( c y ) ~ ' ' - KAcy f :A surement cell, and by recording the resistance values by the same WK 6425 PCA bridge cited above.

Densities and viscosities were measured as previously reported (5).

Karl-Fischer titrations were performed with an automatic titra- tion system (Crison model KF 431) equipped with a digital buret (Crison model 738).

Solutions of electrolytes at different concentrations were ob- tained by successive dilution of stock solutions, freshly prepared by weight; concentrations in volume were then calculated from weight concentrations and densities.

Conductivity readouts were recorded when they become invari- ant with time; this took about 30 min for each measurement.

Several independent solutions were prepared and as many runs as necessary were performed to ensure the reproducibility of the results. Solvent conductivity corrections were applied to all the data at the different temperatures.

Results and discussion The measured equivalent conductivities and the corre-

sponding molarities of solutions for the chosen salts in ED

where the symbols have their usual meaning (8). The above equation provides the limiting equivalent con-

ductivity A,, the ionic association constant K , (dissociation constant K = K,'), and the interionic distance parameter i. The calculations were performed on a computing program by means of an iterative procedure. The initial A, values were obtained from an Onsager plot at each :elected tempera- ture, and the first a value was fixed at 5 A. Generally, only a few iterations were necessary to obtain the final results.

The dissociation constant The K values provided by the Fuoss-Hsia theory are

summarized in Table 1 for all the chosen electrolytes and for any selected temperature in the range from - 10 to +80°C.

'Supplementary Material available: Tables 1-7 (7 pages) of ex- perimental conductivity measurements and thermodynamic data may be purchased from: The Depository of Unpublished Data, Document Delivery, CISTI, National Research Council Canada, Ottawa, Canada K I A 0S2.

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CORRADINI ET AL

FIG. 1. Experimental dissociation constant (K mol-' dm-') of some electrolytes in ethane-1,2-diol at different temperatures

TABLE 3. K,,;,, and corresponding values of r,,:,, for the dissocia- tion of some electrolytes in ethane-1,2-diol

Equation [Z] Harned's theory I Solute Kn,,, t,,,,, Km,m rmax

15

NaBPh, 7.04 X lo-' 33.9 3.09 X lo-' 34.3 -- - PhlPBr 6.08 X lo-' 34.0 2.77 X lo-' 33.5

- NaBr 1.03 X lo- ' 29.4 5.39 X lo..' 33.0 ' - 1 5 -

HPi

NaPi 8.68 X lo-' 34.1 3.81 X 10-"4.1 2 HPi 2.49 X 34.4 2.47 X 38.4

NaDr

- 4 5

1 NaBPhi NaPi Ph<PBr

Each set of dissociation constant values for each solute was !

fitted by means of the integrated van't Hoff equation

which represents the most reliable data-fit model for anal- t ("C> yses of this type. In fact eq. [2], whose a, coefficients for each electrolyte in this solvent are reported in Table 2, repro- duces the experimental values of Table 1 with a good ap- I proximation, as one can deduce from the standard deviation values cr(1n K) summarized in the last column. 0 1 Figure 1 reproduces the trend of experimental K values and k the best-fitting curves expressed by eq. [2]. A brief exami- 7

I

nation of this figure provides some particularly interesting suggestions that may be pointed out as follows.

- i I

1. The dissociation of picric acid and of ion pairs of the other electrolytes shows a generally convex trend of the K l o o [ vs. T curves and, as a consequence, all the curves are char- d -150 - acterized by a relative maximum in the temperature range 1 investigated. / , \ Ph<PBr

2. The two precursor reference electrolytes, NaBPh, and I

Ph,PBr, show slightly different dissociation constant values - 10 20 50 80 over all the studied temperature range, with a moderately high value for the sodium salt. Probably, the large delocalization t ("C> of the electrical charge on the "bolaform" tetraphenyl ions FIG, 2 ~~~~~d~~~~ on the temperature o f@ (k j rnol-') (top) reduces the degree of interaction with other charged spe- and AS' (J "101-I K-I) (bottom) for the dissociation of some elec- cies, releasing in this way the counterion in solution and trolytes in ethane-1,2-diol.

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1268 CAN. J . CHEM. VOL. 71, 1993

TABLE 4. Limiting equivalent conductivities (Ao/cm2 S mol-') for some electrolytes in ethane- 1,2-diol at different temperatures

t/oC NaBPh4 Ph4PBr NaBr NaPi HPi

TABLE 5. Coefficients bj and standard deviations u(Ao) of eq. [5] for some electrolytes in ethane- 1,2-diol

Solute bo b, b2 x 10' b3 x 10' 1 0 ~ a ( ~ " )

NaBPh, -121.25 1.65 -7.47 1.12 0.44 Ph,PBr -155.19 2.08 -9.27 1.38 1.9 NaBr -32.91 0.960 -6.14 1.14 3.1 NaPi -184.29 2.33 -9.88 1.41 1.8 HPi 833.86 -7.56 2.11 -1.64 1.9

freeing it from the electrical attractions responsible to a large extent for ion-pair formation.

3. The higher K values are observed for NaBr and NaPi, showing these electrolytes to have similar behaviour in E D solutions. A probable explanation for this experimental evi- dence could be the relative strength of the solvation bonds towards the different ions. In fact, the sodium ion appears strongly solvated in these solutions and, as a consequence, the solvation shell could mask the central ion towards the counterions. Similar considerations may apply for the sali- fiable anions, Br- and Pi- respectively, taking into account that on progressively increasing the ionic dimensions may observe a progressive decrease in the relative strength of the solvation network; this should lead to a parallel decrease in the dissociation constant values of the electrolyte consid- ered.

Table 3 reports a comparison of the K,,,,, and the corre- sponding t,,, values for these electrolytes. These values have been obtained by fitting eq. [2] and applying Harned's the- ory (9), but poor agreement is observed in this case for the weak electrolyte HPi.

Starting from eq. (21, the thermodynamic data for the ap- parent dissociation reaction of picric acid (10) and the true dissociation of other electrolytes in ED solutions were eval- uated by applying the standard equations in the form:

[4] A s o = R[ao + 2a,T + a,(l + In T ) ]

where the ai terms are the coefficients of Table 2. The re- sults are summarized in Tables 6 and 7 of the Supplemen- tary ate rial^ and in graphic form in Fig. 2.

As can be noted, many uncertainties affect AGO, AH0, and As0 values, owing to the experimental errors in K evalua- tion and partly associated with the interpolating function K = K ( T ) , i .e . , the van't Hoff equation [ 2 ] .

In spite of these difficulties, the thermodynamic data could be a powerful tool in accounting for the solute-solvent in- teractions. As appears from Fig. 2 , enthalpic and entropic variations seem to be comparable in magnitude on the whole for all the salts, excluding HPi, which is a medium-weak electrolyte in ED solution. However, the common trend of Fig. 2 is represented by a negative temperature coefficient dAY/dT, where Y = H O and S O respectively.

We next attempt to obtain some useful structural infor- mation by considering the entropy changes in detail. One may assume that at the highest temperatures an ordered structure exists in the neighbourhood of the charged solute species, in the form of ion pairs or free ions. This, however, is in ap- parent contrast to the thermokinetic steady state that is reached at each selected temperature.

A reliable explanation probably lies in the decreasing value of the dielectric constant of the solvent as the temperature increases ( 3 ) , reducing in this way the electrostriction ef- fects between moving species. Furthermore, the dramatic decrease in the viscosity with rising temperature ( 1 1 ) should provide a considerable decrease of the mechanical friction and viscokinetic delay for all constituent species of the sys- tem, i.e., ion pairs, free ions, and molecules. This situation should facilitate the arrangement and the correct orienta- tion, induced by the strong and thermally unaffected elec- trical fields of the charged species, of the solvent molecules forming the solvation shell.

It should be noted that ED probably solvates anions by a more effective hydrogen bonding network, and cations through dipole and induced-dipole interactions. Thus, at the highest temperatures, its solvation power seems to increase with the size and polarizability of the ions in the series

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FIG. 3. Limiting ionic conductivities (hi/cm2 S mol-') of some species in ethane-1,2-diol at different temperatures.

FIG. 4. Interionic distance parameter (:/A) versus temperature for some electrolytes in ethane-1,2-diol at different temperatures.

1

Br- < BPh,- < Pi- and H' < Na' < P ~ , P + . The negative charge on the Pi- anion is widely spread over all three nitro groups and hence is more delocalized than is the case for other isocharged species. It is to be expected, therefore, that the first anion should be solvated by ED molecules more strongly than the others.

From these arguments and from the evidence obtained about the chosen electrolytes, it may be concluded that the dissociation of salts in ED solutions is a process controlled by enthalpic rather than entropic factors. The limiting equivalent conductivity

Table 4 shows the limiting equivalent conductivities (A,) obtained by the Fuoss-Hsia equation applied to these sol- ute-solvent systems. These values, too, being strictly re- lated to the solute dissociation constant, are strongly dependent on temperature variation and on thermomechan- ical properties of the solvent.

-- - HPi

I I I

The A, values vs. temperature were fitted by a polyno- mial equation of the type (12)

3

which reproc&es the experimental data within an average uncertainty AA, , evaluated as follows:

where N is the number of experimental points, equal to 2 0.13 cm' S mol-I.

Table 5 summarizes the bi ( i = 0, 1, 2 , 3) coefficients of eq. [5] along with the standard deviations u(Ao) for each electrolyte. The trend A, vs. t/OC for these species is char-

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1270 CAN. J . CHEM. VOL. 71, 1993

TABLE 6. Ionic mobilities (h;/cm2 S mol-') of some species in ethane- 1,2-diol at different temperatures

t l " ~ P ~ , P + Naf H + Br- Pi-

acterized by a continuous and regular increase with temper- ature for all the selected electrolytes.

The single-ion conductivities were evaluated by splitting the limiting equivalent conductivities (A,) into ionic contri- butions on the basis of the fundamental assumption of a ref- erence electrolyte (Ph,PBPh, in this case), using the following relationships (1 3):

In practice, one assumes that the two voluminous tetra- phenyl derivative ions (opposite charge but similar struc- ture) can be characterized by the same thermodynamic behaviour, and therefore by the same ionic activity coeffi- cients and the same ionic mobility when dissolved in any solvent and at any temperature.

The limiting ionic conductivities (A;) for all the species investigated in this work were obtained by applying the re- lations:

starting from the smoothed A. values fitted by eq. [ 5 ] . The results of this analysis are reported in Table 6 and dis- played, in a graphic form, in Fig. 3.

For comparison purposes, Table 7 shows the limiting ionic conductivities in some different solvents. As is particularly evident, the hydrogen ion appears to be the species with the highest mobility in all the cases collected in Table 7. For the Na+ ion, for example, the limiting conductivity values seem to be comparable with those obtained in HMPT solutions,

even if generally lower than the values obser\ solvents characterized by solvent properties suc ascribable to ED, but where the thermokinetic r, effects are not equal to those provided in this solvr one may observe that the mobility values of tetraphe picrate ions in ED are the lowest of those ions lii Table 7.

The Walden products, Airlo, of the selected ions art ported in Table 8. As one can see, the rule appears to substantially obeyed over this wide temperature range fro the large tetraphenyl derivatives to the picrate anion, in cluding the relatively small ~ a + ion, which is probably strongly solvated. The greatest exception to this rule, lim- ited because its empirical nature is nowadays largely uti- lized to assess the values of ionic mobilities under different experimental conditions, is represented by the hydrogen ion.

The imperfectly defined chemical nature of this species in nonaqueous solvents, in conjunction with the observed high values of ionic mobility in almost all the alcoholic solvents, suggests a hypothetical mechanism for electrical conductiv- ity in these media similar to the well-known mechanism proposed for water solutions. In this mechanism the hydro- gen ion could act alternatively as structure maker and struc- ture breaker in the network bonding between neighbouring solvent molecules, in order to explain the transport phe- nomenon described above.

The interionic distance parameter Table 9 summarizes the ion-size fitting parameter a pro-

vided by the Fuoss-Hsia equation for analysis of the ex- perimental conductivity data for the selected electrolytes in this nonaqueous solvent (ED). As one can see from Fig. 4 , the trend of a vs. tl°C seems perfectly delineated with re- spect to the temperature variable, and it follows those trends described above for K = K(T).

However, a careful examination of the ion-size fitting parameter i and the K values of Table 1 suggests a prudent evaluation of the former quantity. In fact, Skinner and Fuoss (14) studied the conductometric behaviour of NaBPh, in water, and these authors found a = 6.64 + 0.06 A for KA = 0 . Later, Covington and Tait (15) reexaminedo the same problem, and provided the value A = 9.9 + 0 . 9 A for KA = 0 . These authors also showed that the calculated ion size i = 6.64 A as determined byoSkinner and Fuoss for KA = 0 can be increased to ;i = 10 A, using the experimental data of Skinner and Fuoss if a small association constant is im- posed. From these considerations, it is clear that the ion-size parameter 2 is not completely independent of the associa- tion constant in solution, because an identical set of con- ductivity data can be fitted with a smaller ;; if it is assumed that any association phenomenon takes place in solution, and vice versa.

Moreover, for those electrolytic solutions with a consis; tent association investigated here, determination of the a parameter and K values should be less ambiguous. For the NaBPh, electrolyte in ED solutions, our ;; values seem to agree with those reported by other authors working in DMSO (16), which is an aprotic but almost isodielectric solvent if compared with ED.

Conclusions

Some closing notes can now be written about our elec- troanalytical studies in ethane-1,2-diol.

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TABLE 7. Limiting equivalent conductivities (h;/cm2 S mol-I) of some ions in different solvents

CH,OH DMAC DMF DMSO HMPT TMU PC ED H20 - -

H + 142.2 - - - - - 12.9 19.77 349.8 Na+ 42.5 25.8 29.9 14.2 5.7 15.1 9.46 3.47 50.1 Br- - 43.2 53.6 23.4 18.2 30.1 18.90 5.08 78.1 Pi- 49.2 31.5 - 16.7 - - 12.50 1.59 30.4 BPh4- - - - - 6.7 - 8.10 16.02 1.18

Ref. 18 19 20 2 1 22 23 24 This work 25

TABLE 8. Walden products of some ionic species in ethane-1,2- diol at different temperatures

t r C Ph4P+ Na+ H+ Br- Pi-

TABLE 9. Interionic distance centre-to-centre parameters (;/A) of some electrolytes in ethane-1,2-diol at different temperatures

t r C NaBPh, Ph,PBr NaBr NaPi HPi

At first, we found that all the salts studied are moderately dissociated in this solvent medium, this fact being expected because of the medium dielectric constant of the solvent at all the temperatures investigated. The most outstanding fea- ture of the dissociation constants reported in this work is that the salts containing larger ions show a progressive amount of association. However, excluding the ionogen solute HPi, the dissociation constant seems to decrease with increasing size of the anion, and the decrease is also observed in the case of the largest cation if compared to that of the smaller cat- ion. These observations can be accounted for by assuming that the stabilization of the anions in ED solution increases in the order BPh,- < Pi- < Br-, and the stabilization of the cations is in the order P ~ , P + < ~ a + . Thus, the behaviour in ED of the selected sodium salts appears perfectly consistent with measurements in other simple alcohols (17) where K decreases with the increasing anion size.

Concerning the single-ion conductivity, it should be noted that the mobility of the small Na' cation is less than that of the Br- anion. This fact suggests that the Na' ion could be more strongly solvated by ED molecules than the Br- spe- cies. Furthermore, the transport behaviour of Pi- and PH,P+ = BPh,- ions appears small and slightly different in this solvent. A reliable explanation for this can probably be found in the low-density surface charge, masked by an ex- tensive delocalization, and from the high viscosity of the medium, which makes difficult any ionic migration in so- lution.

Acknowledgments

It is a pleasure to thank Prof. C. Preti for his continuous encouragement to carry out this work and for constructive suggestions concerning this paper. L.M. wishes to thank the Hospal-Dasco s.p.a. (Modena, Italy) for the award of a re- search fellowship. We also gratefully acknowledge the fi- nancial support of The Consiglio Nazionale della Ricerche (C.N.R.) of Italy.

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